Elastic wavefield separation by combining pseudo-Helmholtz decomposition operator and optimization expansion strategy in VTI media

In anisotropic elastic media, the effective separation of P/S wave has a significant meaning for understanding the propagation characteristics of different types of seismic waves and mitigating crosstalk artifacts in seismic imaging and inversion. Present wavefield separation techniques primarily rely on divergence- and curl-like operators, low-rank approximation, pseudo-Helmholtz decomposition, and so on. The corresponding computational accuracy and efficiency need to be further improved. To address this issue, we propose an effective wavefield separation method for Vertical Transversely Isotropy (VTI) elastic media by integrating the pseudo-Helmholtz decomposition operator with an optimization expansion strategy. First, we employ eigenform analysis method to derive the corresponding eigenvalue and eigenvector for the elastic VTI Christoffel equation. Then, we calculate the approximated eigenvalue and eigenvector using Taylor-expansion method and further construct the wavefield separation operator and process by combining the pseudo-Helmholtz decomposition operator, the optimization polynomial expansion strategy and the unit vector estimation method for VTI elastic media. Finally, the accuracy advantage of our proposed method is verified by eigenvalue approximation accuracy analysis and wavefield separation operator accuracy analysis. Several modeling examples demonstrate that, compared to the existing advanced wavefield separation method, our proposed approach can produce high-accuracy wavefield separated results.